Problem: $g(n) = -6n^{2}+f(n)$ $f(n) = 5n^{2}$ $h(x) = 3x+7-2(f(x))$ $ g(h(-1)) = {?} $
Answer: First, let's solve for the value of the inner function, $h(-1)$ . Then we'll know what to plug into the outer function. $h(-1) = (3)(-1)+7-2(f(-1))$ To solve for the value of $h$ , we need to solve for the value of $f(-1)$ $f(-1) = 5(-1)^{2}$ $f(-1) = 5$ That means $h(-1) = (3)(-1)+7+(-2)(5)$ $h(-1) = -6$ Now we know that $h(-1) = -6$ . Let's solve for $g(h(-1))$ , which is $g(-6)$ $g(-6) = -6(-6)^{2}+f(-6)$ To solve for the value of $g$ , we need to solve for the value of $f(-6)$ $f(-6) = 5(-6)^{2}$ $f(-6) = 180$ That means $g(-6) = -6(-6)^{2}+180$ $g(-6) = -36$